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###############################################
## Soetaert and Herman (2008) ##
## A practical guide to ecological modelling ##
## Chapter 6. ##
## Model solution - numerical methods ##
## Chapter 6.6.3 ##
## 0-D estuarine zooplankton model ##
###############################################
#-----------------------#
# the forcing function: #
#-----------------------#
fZooTime = c(0, 30,60,90,120,150,180,210,240,270,300,340,367)
fZooConc = c(20,25,30,70,150,110, 30, 60, 50, 30, 10, 20, 20)
# The model, integrated with EULER
euler <-function(start,end,delt,g,k)
{
times <- seq(start,end,delt)
nt <- length(times)
ZOOsea <- approx(fZooTime,fZooConc, xout=times)$y
ZOO <- 5
out <- matrix(ncol=3,nrow=nt)
for (i in 1:(nt-1))
{
decay <- g*ZOO
input <- k*(ZOOsea[i] - ZOO)
out[i,] <- c(times[i],ZOO, input)
dZOO <- input - decay
ZOO <- ZOO + dZOO *delt
}
colnames(out) <- c("time","ZOO","input")
return(as.data.frame(out))
}
out <-euler(0,365,0.1,k=0.015,g=0.05)
par (oma=c(0,0,0,2))
plot(fZooTime,fZooConc,type="b",xlab="daynr",
ylab="gC/m3",pch=15,lwd=2,
main="Zooplankton model")
lines(out$time,out$ZOO,lwd=2,col="darkgrey")
legend("topright",c("Marine zooplankton","Estuarine zooplankton"),
pch=c(15,NA),lwd=2,col=c("black","grey"))
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